The age of the father 4 years ago was 5 times the age of his son. If the sum of their present ages is 44 years. What is the present age of his son ?

Options

A. 6 years
B. 10 years
C. 4 years
D. 8 years

Answer

To solve the problem, we will use algebra to represent the ages of the father and son. Let's denote the present age of the son as \( x \) years.

### Step-by-Step Solution:

1. **Define Variables:**
Let the present age of the son be \( x \) years. Therefore, the present age of the father will be \( 44 - x \) years, since the sum of their present ages is 44 years.

2. **Set Up the Equation Based on the Given Information:**
According to the problem, the age of the father 4 years ago was 5 times the age of his son at that time.
- The father's age 4 years ago: \( (44 - x) - 4 = 40 - x \)
- The son's age 4 years ago: \( x - 4 \)

We can set up the equation:
\[ 40 - x = 5(x - 4) \]

3. **Simplify the Equation:**
Expanding the right side:
\[ 40 - x = 5x - 20 \]

4. **Rearranging the Equation:**
Now, we will move all terms involving \( x \) to one side and constant terms to the other side:
\[ 40 + 20 = 5x + x \]
\[ 60 = 6x \]

5. **Solve for \( x \):**
Dividing both sides by 6:
\[ x = 10 \]

6. **Conclusion:**
The present age of the son is \( 10 \) years.